Zero-knowledge proof based on zk-SNARKs applying ω Protocol : zk-FIDNA

Abstract

This paper introduces the Elliptic Curve Homomorphic Digital Signature Algorithm (EHDSA), a novel digital signature scheme that enhances security by leveraging homomorphic encryption. Unlike traditional ECDSA, which generates signatures using the x-coordinate of elliptic curve points, EHDSA employs a homomorphic mapping between elliptic curves and Zn. This mapping conceals the original elliptic curve point information, providing increased security. EHDSA is particularly advantageous in resource-constrained environments due to its reduced signature size, computational speed, and security compared to RSA. Additionally, this paper explores the ω protocol, which utilizes ElGamal Encryption and a Common Reference Domain Set (CRDS) to perform secure zero-knowledge proofs. The protocol’s arithmetic circuit is transformed into a Linear Form Arithmetic Program (LFAP), ensuring efficient proof creation. We also discuss the use of digital signatures for polynomial commitments, ensuring the integrity and authenticity of the commitment process. The integration of EHDSA into the ω protocol significantly enhances the overall security and efficiency of digital signatures and zero-knowledge proofs, addressing fundamental privacy vulnerabilities in traditional ECDSA while maintaining computational efficiency through J-invariant-based curve classification and signature-integrated commitment schemes.